Algebra 1 CC
Assignment #56
Introduction to Exponential Functions
y
1. Consider the exponential function f ( x ) = 10 ( 2 ) .
x
(a) Find the value of f ( 0 ) . What point does this represent on the graph of
y = f ( x) ?
(b) Is this an increasing or decreasing exponential function? How can you tell
based on its equation?
x
(c) Is this function’s average rate of change over the interval −1 ≤ x ≤ 2
x ) 10 x + 7 ? Justify.
greater or less than that of the linear function g (=
(d) Using your calculator, sketch a graph of this function on the axes shown
below. Use the window indicated. Mark the y-intercept.
2. Which of the following is a decreasing exponential function whose y-intercept is 20?
4
3
x
1
2
(1) y = 20  
x
(2) y = 20  
(3) y =
−2 x + 20
1
3
x
(4)
=
y   + 20
3. Graphing a basic exponential can be challenging because of how quickly they grow (or decay). In this exercise, we
will graph one of the most basic.
y
f ( x ) = 2x
(a) Evaluate each of the following and state the coordinate point
that occurs on the graph of f ( x ) based on the calculation.
f ( 0) =
f (1) =
f ( 2) =
f ( 3) =
(b) Evaluate each of the following. Remember your facts about
negative exponents and give the point on the graph of f ( x )
x
.
f ( −1) =
f ( −2 ) =
f ( −3) =
(c) Using the points you found in (a) and (b), graph this function for the domain interval −3 ≤ x ≤ 3 .
4. Classify each of the following exponential functions as either increasing or decreasing and give the value of their yintercepts.
(a) y = 125 (1.25 )
x
3
(b) y = 22  
4
x
5
(c) y = 256  
2
x
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R1.a. Graph the following functions: f ( x=
) x 2 − 8 and g ( x ) = 2 x . Set your window according to the axes
y
below.
15
b. What are the solutions for the equation x 2 − 8 =
0 ?
c. What are the solutions for the equation 2 x = 4 ?
d. What are the solutions for the equation x 2 − 8 =2 x ?
x
10
R2. Decide whether each of the following relations is a function. Explain your answer.
Input
(a) States
(b) States
(c) Families
(d) Families
Outputs
Capitals
Cities
Pets
Last names
R3. If n represents a number, then write an expression for the difference of three times the number after it was increased
by 3 and twice that number.
__________________________________________________________________________________________
1. (a)
f ( 0 ) = 10 This point represents the y-intercept.
(c)
(b) increasing because the base value is greater than 1
(c) greater
(d)
11.6 >10
4.
2.
(2)
3.
(a)
f ( 0) = 1
(a) increasing
(b) decreasing
(c) increasing
R1.a.
f (1) = 2
f ( 2) = 4
f ( 3) = 8
(b)
1
f ( −1) =
2
1
f ( −2 ) =
4
1
f ( −3) =
8
b. x = ± 8
c. -2 and 2
d. (-4, 8) and (4, 8)
R2. (a) yes
(b) no
(c) no
(d) no
R3.
3( x + 3) − 2 x